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A087648
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a(n) = (1/2)*(Bell(n+2)+Bell(n+1)-Bell(n)).
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4
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1, 3, 9, 31, 120, 514, 2407, 12205, 66491, 386699, 2388096, 15589732, 107165081, 773106715, 5836100685, 45981026703, 377230766908, 3215977070706, 28437411817135, 260380616093533, 2464930698184351
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OFFSET
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0,2
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COMMENTS
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Sum of last number in all set partitions of n+1. E.g. The set partitions of 3 are {1,1,1}, {1,1,2}, {1,2,1}, {1,2,2} and {1,2,3}, so a(2) = 1+2+1+2+3 = 9. - Franklin T. Adams-Watters, Jun 07 2006
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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MATHEMATICA
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f[0]=1; f[n_] := Sum[ StirlingS2[n, k]*Binomial[k+2, k ], {k, 1, n}]; Table[ f[n], {n, 0, 20}] (* Zerinvary Lajos, Mar 31 2007 *)
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PROG
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(MAGMA) [(1/2)*(Bell(n+2)+Bell(n+1)-Bell(n)) : n in [0..30]]; // Vincenzo Librandi, Nov 13 2011
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CROSSREFS
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Cf. A000110, A035098, A059606.
Main diagonal of A120057, row sums of A120095.
Column 1 of array in A322770.
Sequence in context: A073724 A151037 A066571 * A086616 A040027 A182968
Adjacent sequences: A087645 A087646 A087647 * A087649 A087650 A087651
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic, Sep 23 2003
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STATUS
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approved
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